This is not going to be a strictly Firefox related entry. I’ll try to suggest some solutions to privacy threats connected with surfing the web. There is not such thing as being anonymous in the Internet, but you may easily make it much harder to track your activity.
Temporary e-mail address
When a website requires you to give your mail in order to register, you can usually expect some spam messages later on. Using a temporary mail is a good solution. You can create a virtual mail account, which forwards mails to your real address only until you remove it. There are plenty of websites offering it, like guerrillamail.com, 10minutemail.com or spambog.com.
I’ll just focus on two with support for Firefox.
Tempomail
Right click and choose tempomail from the context menu.
Enter your real address in the pop-up and in the next step you’ll see the temporary address automatically put in the form.
Perfectly simple and useful.
Gish it!
Pretty similar to Tempomail. Register at the extension’s homepage and install the add-on. Now, when you need to register, just click the Gish it! button in the right-click menu. 
In the pop-up window that appears you get an automatically created virtual e-mail account.
Copy the temporary address, paste it to the registration form and you’re done.
Control cookies
Cookies can be used for tracking your Internet behavior. Therefore, you may want to be able to manually allow websites to install them on you computer.
CS Lite will allow you to easily control cookie permissions. It can be accessed from the statusbar, a toolbar button, or the context menu.
Just click on the icon to allow, block, or temporarily allow the site to set cookies. You can also view, clear or edit the cookies and exceptions by right clicking on the cs lite icon.
For safer browsing you may choose to deny cookies globally and then enable them on a per site basis. You can also download a blocklist that contains a list of untrusted hosts that you may choose to import into FF and block.
The ultimate anti-tracking solution. Tor: anonymity online.
Tor project homepage
Tor works independently from Firefox, but I decided to put it here as it may be a very useful application for those of you, who need absolutely safe Internet websurfing.
Tor is a software project that helps you defend against traffic analysis, a form of network surveillance that threatens personal freedom and privacy, confidential business activities and relationships, and state security. Tor protects you by bouncing your communications around a distributed network of relays run by volunteers all around the world: it prevents somebody watching your Internet connection from learning what sites you visit, and it prevents the sites you visit from learning your physical location. Tor works with many of your existing applications, including web browsers, instant messaging clients, remote login, and other applications based on the TCP protocol.
FoxyProxy
Your IP address is recorded every time you visit a website. Sites like Google tie your searches with your IP address. Every search you perform may be used for gaining some knowledge about you - your hobbies, medical remedies and so on.
FoxyProxy is a Firefox extension which automatically switches an internet connection across one or more proxy servers based on URL patterns. Put simply, FoxyProxy automates the manual process of editing Firefox’s Connection Settings dialog. Proxy server switching occurs based on the loading URL and the switching rules you define.
For even more safety, this extension can also be used with Tor, the project described before.
Don’t send the referring site information
When you click a link, the website you visit can check where you’re coming from. This may be used for example for analysis. If you want to disable sending information on the referrer, RefControl is for you. You can enable referrers on a per site basis.
Other privacy-related apps and add-ons
NoScript (download) - this extension blocks scripting languages globally, protecting you from attacks like XSS, XSRF or CSRF. It can be configured to allow scripts to run on a per domain basis.
LocalRodeo (download) - JavaScript can make your browser connect to a site with a different IP address than originally set. If you don’t use NoScript or want to check even the pages you excluded from NoScript protection, you may find it useful.
SafeCache (download) - segments browser cache, which an be used for tracking your activity.
SafeHistory (download) - restricts the marking of visited links on the basis of the originating document, defending against web privacy attacks that remote sites can use to determine your browser history at other sites.
Even more stuff
8 Firefox extensions towards safer browsing
Porn addict’s toolbox: 100 Tools and Resources to Keep Your Privacy and Security